This invention relates to a superconducting coil system and, more particularly, to a technique of suppressing and reducing generation of current imbalance in a superconducting strand.
FIG. 1 shows, in a cross-section, an illustrative cable-in conduit conductor (CICC) constituting a conventional superconducting coil system.
Referring to FIG. 1, the cable-in-conduit conductor is comprised of tens to hundreds of yarned (or twisted) superconducting strands packed in a stainless steel conduit in the form of a pipe.
In a cable-in-conduit conductor, the void ratio, representing the ratio of an area in a cross-section excluding an area occupied up by the strands, is usually set to approximately 35 to 37% (see Takahashi et al., xe2x80x9cChromium Plating Thickness Dependency of Cable-in-conduit Conductor on Coupling Lossxe2x80x9d, . Extended Abstract to the 52nd Autumn Meeting of 1994 of Low-Temperature Superconducting Association [Teion Kogaku Chodendo-Gakkai], A3-6, page 225, xe2x80x98literature 1xe2x80x99).
The liquid helium (He) or supercritical He is allowed to flow between these strands to cool the strands to permit the current to flow therein in a superconducting state.
The conduit performs the role of securing a flow channel for He, in addition to the role of supporting the gigantic electro-motive force exerted on the conductor.
FIG. 2 shows an illustrative method for producing this sort of the CIC conductor.
Referring to FIG. 2, each strand is of a diameter of 0.76"PHgr" [mm] and has embedded in the mid portion thereof a superconducting filament formed of copper and NbTi, Nb3Sn or the like.
In the embodiment of FIG. 2, three such strands are twisted together to form a sole twisted yarn. Three such twisted yarns are twisted together to form a sole twisted wire. This operation is repeated twice resulting in a twisted cable, and ultimately six resultant cables are accommodated within a 23.0xc3x9727.6 mm sized conduit.
Thus, in the embodiment of FIG. 2, 3xc3x973xc3x973xc3x973xc3x976=486 strands are used.
There are several reasons of using a large number of twisted yarns.
One of such reasons is reducing AC loss. Eddy current flows on the surface of a conductor placed in an AC circuit or in a changing magnetic field as time lapses. This phenomenon is known as the skin effect.
The surface of the strand is formed of copper, as shown in FIG. 2. Thus the eddy current is apt to flow on the strand surface such that heat is evolved by the resistance of copper to detract from stability of the superconducting coil. Therefore, a strand of small diameter is used for reducing the eddy current loss.
Meanwhile, if the characteristic depth (penetration depth) of the skin effect is xcex4 and the strand diameter is d, a designing standard is given by the following inequality:
d less than xcex4xe2x80x83xe2x80x83(1)
The strand of such fine diameter is satisfactorily compatible with machining NbTi or the like into a filament.
Another reason of twisting (or yarning) a number of strands is that, since the conductor is intended for fabricating a coil, a bending operation is required.
If the strand is not twisted, it is poor in bendability and might occasionally encouter fracture.
During coil production, a coil is bent in one direction, as a result of which the coil length as measured on its inner diameter side differs from that as measured on its outer diameter side.
If the strand would be not twisted, it would be stretched on its outer diameter side while being contracted on its inner diameter side.
The twisting operation is performed for preventing lowering of superconductor characteristics due to such non-symmetrical structure.
The CIC conductor, thus fabricated, is wound to a pre-determined shape for producing a coil.
If the coil is used for an AC circuit or the like, it is preferred that the strands be electrically insulated from one another for the above reason. The reason is that, if the surfaces of the strands are electrically connected to one another, the plural strands can be regarded as a conductor with a larger surface area and a larger volume, so that the eddy current loss W is increased. The eddy current loss is proportionate to the square of the characteristic size such that
Wxe2x88x9dd2xe2x80x83xe2x80x83(2)
In the above equation (2), W represents the eddy current loss and d represents the strand diameter.
Since there are, in effect, a large number of contact portions in a sole strand, the eddy current flows in a complex pattern.
For the above reason, in preparing an NbTi-30KA grade coil (DPC-U) by a CIC conductor in the demonstration poloidal coil (DPC) project of Japan Atomic Energy Research Institute, referred to hereinafter as JAERI, each strand is insulated by Formvar insulation.
That is, the surface of the strand shown in FIG. 2 is coated with a Formvar insulating material to a thickness of several micrometers (see FIG. 3). By coating the strand surface with the insulator, the individual strands are insulated satisfactorily from one another.
By employing such structure, a superconductor coil of high stability and low eddy current loss with only little AC loss have been expected to be producible. In the case of a superconductor coil used in an AC circuit, although the AC losses may be enumerated by hysteresis loss and proximity effect loss etc., in addition to the eddy current loss, the eddy current loss is predominant among these AC losses.
However, experiments on DPC conducted by the JAERI was not successful, as will now be explained.
Before an experiment on passing the AC current, an experiment was conducted using a pulse-shaped current waveform (see FIG. 4). Due to excitation of a sole coil, the waveform of the magnetic field generated by the coil is analogous to FIG. 4.
Consequently, the rate of change of the magnetic field (flux density) dB/dt during a time period 0 to t1 (time differential of magnetic field) is found. In an experiment, the time from 0 to t1 is controlled by an external power source and the rate of change of the magnetic field dB/dt was varied for finding data such as stability of the superconducting coil.
Thus it was found that, in this superconducting coil, the value of the rate of change of the magnetic field dB/dt which permits stable operation was approximately one thousandth of the initial design value.
It was intended at the outset to achieve a world record in connection with the rate of change of magnetic field dB/dt. However, in fact, the coil quenching occurred at a value of the rate of change of magnetic field dB/dt which was significantly lower than that with the conventional coil.
The reason therefor was checked precisely by researchers of the JAERI, manufacturers and universities. It was found that the currents flowing in the individual strands are not the same but large current imbalance exists. The results of the analysis are substantially as follows:
FIG. 5 shows an equivalent circuit in case two strands are used.
Referring to FIG. 5, L1 and r1 denote self-inductance and resistance of strand 1, L2 and r2 denote self-inductance and resistance of strand 2, respectively, and M denotes mutual inductance.
The circuit network equation is given by the following equations (3) and (4):
xe2x80x83V=r1xc2x7i1+jxcfx89L1xc2x7i1+jxcfx89Mxc2x7i2xe2x80x83xe2x80x83(3)
V=r2xc2x7i2+jxcfx89L2xc2x7i2+jxcfx89Mxc2x7i1xe2x80x83xe2x80x83(4)
In the above equations, xcfx89 and j denote the oscillation frequency of the circuit and an imaginary number of j2=xe2x88x921, respectively.
By solving the equations (3) and (4) with respect to the currents i1, i2, the following equation (5) is derived:                                           i            1                                i            2                          =                                            r              2                        +                          jω              ⁡                              (                                                      L                    2                                    -                  M                                )                                                                        r              1                        +                          jω              ⁡                              (                                                      L                    1                                    -                  M                                )                                                                        (        5        )            
Since the strand is in the superconducting state, r1=r2=0 in the equation (5), and thus the current ratio of the two strands is given by the equation (5xe2x80x2):
i1/i2=(L2xe2x88x92M)/(L1xe2x88x92M)xe2x80x83xe2x80x83(5xe2x80x2)
As will be understood from the explanation of the method for producing the CIC conductor of FIG. 2, since the stands are wound tightly each other, the mutual inductance M assumes a value which is extremely close to the self-inductance L1 or L2.
In addition, the self-inductance L1 is not completely equal to the self-inductance L2 and the two values usually differ slightly from each other.
The results of measurement on DPC conducted by the JAERI have revealed that fluctuations in the self-inductance were not more than approximately 1% and that the value of mutual inductance was on an order of 99% of the value of self-inductance. Substituting this into the above equation (5xe2x80x2), the following equation (6) is derived:
i1/i2=(101xe2x88x9299)/(100xe2x88x9299)=2/1xe2x80x83xe2x80x83(6)
Thus it is seen that a minor difference in inductance doubles the current ratio between different strands.
On the other hand, there is a critical current Ic for the current flowing in the strand, such that, if the current exceeding a pre-determined value flows, quenching occurs.
That is, in the case of the above-described DPC arrangement of the JAERI, such quenching is produced if the current in several of the entire of 486 strands exceeds the critical current Ic.
This induces quenching of the entire coil, as a result of which the value of the current that can be caused to flow stably was as low as approximately about one-thousandth of the value of the initially intended rate of change of magnetic field dB/dt.
The analysis of this phenomenon is vigorously researched at present and the results of the researches are being published in, for example, the following publications:
(1) Ando et al., xe2x80x9cAnalysis of Current Imbalance in the Presence of the Contact Point within the Twisted Superconducting Conductor for AC and Pulsesxe2x80x9d, Extended Abstract to the 52nd Autumn Meeting of 1994 of Low-Temperature Superconducting Association, E1-22, page 119, xe2x80x98literature 2xe2x80x99).
(2) Koizumi et al., xe2x80x9cPhenomenon of Current Imbalance in 30KA grade NbTi Conductorxe2x80x9d, Extended Abstract to the 52nd Autumn Meeting of 1994 of Low-Temperature Superconducting Association, A3-10, page 229, xe2x80x98literature 3xe2x80x99).
(3) Toida et al., xe2x80x9cOn the Quenching Characteristics upon AC Conduction in Twisted Superconducting Conductor for ACxe2x80x9d, Extended Abstract to the 52nd Autumn Meeting of 1994 of Low-Temperature Superconducting Association, A3xe2x80x943, page 222, xe2x80x98literature 4xe2x80x99).
Of these, Koizumi et al.(JAERI) point out in the literature 3 the possibility of the current as much as 7.1 times the mean current value having flown through several strands due to cooling medium temperature dependency of the quenching current value. It is estimated that, in a DPC-U conductor, disturbance in self-inductance of the strand is estimated to be 0.12%, or 0.06% in strand length.
Based on the results of the above analysis, the strand surface of the recently produced CIC conductor is plated with chromium, as shown in FIG. 3, instead of Formvar insulation.
If the strand surface is plated with chromium, the strands are not insulated satisfactorily from one another, so that the eddy current loss is increased, as explained previously. However, the eddy current loss incurred is smaller than the case where the copper surface remains by itself because chromium is lower in electrical conductivity than copper.
On the other hand, if the current in some strands exceeds the critical current due to current imbalance in the strands, quenching is initiated. In general, quenching is initiated at a certain portion of the strand.
Since an electrical voltage is generated due to electrical resistance at the strand portion where quenching has occurred, current diversion or commutation (current splitting) occurs from the contact portion of the chromium plating to another element (strand).
FIG. 6 shows the manner of current splitting due to the quenching in two strands. In FIG. 6, R1 denotes a resistance caused by quenching generated due to a current exceeding the critical current Ic, and Rc denotes a contact resistance of the chromium plating.
The current I1 flowing in a strand 1 is split at the quenching portion in amounts determined by resistances R1, Rc. The larger the resistance R1, the larger is the proportion of the current flowing in strand 2.
In effect, this phenomenon occurs between a number of strand pairs. By such current splitting, the strand currents are rendered uniform to enable the coil to be driven stably.
However, if such structure is used, it becomes necessary to check the thickness of the chromium plating or current diversion dependent upon the thickness of the chromium plating. This complicates the analysis and necessitates experiments. Thus study is described in the above literatures 1 and 4 and in the following literature.
Tsuchioka et al., xe2x80x9cAnalysis of Current Imbalance between Strands in Cable Conductorxe2x80x9d, Extended Abstract to the 52nd Autumn Meeting of 1994 of Low-Temperature Superconducting Association, E1-24, page 121, xe2x80x98literature 5xe2x80x99).
After all, the gist of this line of investigations resides in the following: that because of current imbalance in the strands, it is crucial in designing the CIC conductor to adjust chromium plating etc. depending on the design requirements for the coil, although the eddy current loss could be reduced by complete insulation.
However, no satisfactory designing method for making adjustment of chromium plating in accordance to the design requirements required of the coil has been established to date.
If the superconducting strands are electrically insulated from one another, as explained above, the strand circuit forms a parallel circuit, thus producing current imbalance resulting in quenching.
A superconducting strand is formed by fine wires of superconductor, such as NbTi, embedded in copper or the like. As the case may be, the strand surface is coated with an insulating material, such as Formvar etc., or plated with Ni or formed of copper itself.
The current imbalance is induced in a strand by the fact that the self-inductance and the mutual inductance between the strands differ from one another slightly, that is by up to about 1% or less, and that, since the circuit is a superconducting circuit, the resistance components scarcely exist in the circuit. Detailed discussions on this subject are found in S. Ando et al., xe2x80x9cExperimental Researches Concerning Current Imbalance Flowing in Twisted Superconductors for Large AC and Pulse Currentxe2x80x9d, thesis presented to Society of Electricity [Denki-Gakkai Ronbunshi] A, pages 223 to 238, vol.115-A, No.3, 1995 xe2x80x98literature 6xe2x80x99.
In light of the above, the present inventor has proposed in JP Patent Application No. 6-316071 a method of eclectrically insulating the individual strands of current leads of a superconducting coil system and connecting them to respective superconducting strands.
With the method proposed in the above JP Patent application 6-316071, the resistances of the current leads are inserted in the electric circuit of the superconducting strands, thus eliminating the current imbalance.
With the proposed method, since the strand temperature ranges from room temperature to low temperature, the resistance of the current leads necessarily exist unless a material which becomes superconducting at room temperature is found.
In the present-day designing of the current leads, the above proposed method overcomes the current imbalance in the strands to assure stable operation of the superconducting coil, taking into account parameters of the superconducting magnets energy storage system (SMES) thought to be the largest market for application of the superconducting coil for domestic (commercial) application.
However, the current imbalance cannot be prohibited with the commercial frequencies (60 Hz to 50 Hz) by the resistance of the current lead.
The superconducting coil is used because it has no electrical resistance (electrical resistance=0). In future research and development, the target will necessarily be to lower the resistance of the current lead portions.
Since the major portion of the electric power is utilized at a commercial frequency, it is desirable that the superconducting coil be usable at the commercial frequency.
Consequently, the superconducting coil needs to be driven at the commercial frequency. In addition, for stable driving, it is essential to prevent the current imbalance in the superconducting strands.
The present invention has been made on the basis of the above-described recognition acquired by the present inventor. It is an object of the present invention to provide a superconducting coil system which can be driven at a commercial frequency and which prohibits the current imbalance from being produced. Further objects will become apparent in the entire disclosure.
For accomplishing the above object, the present invention provides a superconducting conductor or coil system characterized in that two strands are arranged so as to pass through a hollow portion of a substantially cylindrical hollow magnetic member so that the current will flow in the strands in mutually opposite directions.
Also, according to the present invention, n pairs of strands totalling at 2n strands are preferably arranged as pairs so as to pass through hollow portions of an nxc3x97n (generally mxc3x97n) array of substantially cylindrical hollow magnetic members so that the current will flow in each strand pair in mutually opposite directions.
Further, according to the present invention, n pairs of strands totalling at 2n strands are preferably arranged as pairs so as to pass through hollow portions of a 2-row by n-column array of substantially cylindrical hollow magnetic members so that the current will flow in each pair of said strands in mutually opposite directions.
According to the present invention, the above strands are driven by a power source of a commercial frequency.
Moreover, according to the present invention, a plurality of, herein 2n, lead wires making up current leads are connected, without being bundled together, to 2n stands arranged for passing through the hollow portions of the substantially cylindrical hollow magnetic members (i.e., cores) arranged in an nxc3x97n (generally mxc3x97n) array configuration.
According to the present invention, iron cores or ferrite cores are used, which are usually termed as wound core and prepared by coaxially winding a large number of thin sheets to form a hollow portion, as shown in FIG. 7. That is, the wound core has a center through-hole and substantially cylindrical in shape.
A plurality of cores shown in FIG. 7 are used and arrayed preferably in a matrix configuration as shown in FIG. 8.
Referring to FIG. 8, 3xc3x973=9 cores are arranged in a matrix configuration. A plurality of, herein six, strands are numbered from (1) to (6) as shown. The current is denoted by solid lines interconnecting the same strand numbers and flows from above towards below in the drawing.
Two strands are passed through the hollow portions of the core. The current directions in the two strands in the same through-hole are opposite to each other.
If the configuration shown in FIG. 8 is used, 2n strands are used for nxc3x97n=n2 cores, (in general, mxc3x97n cores).
According to the present invention, the current imbalance between strands can be suppressed and decreased to a negligible level, while driving becomes possible with a commercial power source, as will be explained subsequently.
If the strands are electrically insulated from one another, the strand portions passing through the cores need not be in the superconducting state. For example, these strand portions can be at near the temperature of liquid nitrogen. In such case, copper wires, for example, in place of NbTi wires, are passed as strands through the core(s).
According to the present invention, if the cores are arranged as shown in FIG. 14 (2 rowsxc3x974 columns=2xc3x97n, n=4), preferably, 2n cores suffice for 2n strands.
Meritorious Effects of the invention can be summarized below, but not limited thereto. Further advantages will become apparent in the entire disclosure.
According to the present invention, as described above, there is achieved a meritorious effect that, since superconducting strand pairs through which flows the current in mutually opposite directions are arranged between cores, it becomes possible to suppress and reduce the current imbalance in the strands. According to the present invention, there is also achieved an additional advantage that the superconducting coil can be driven at the commercial frequency.
Moreover, according to the present invention, the cores through the hollow center of each of which a pair of strands pass, in which flows the current in mutually opposite directions, can be arranged in the nxc3x97n (generally mxc3x97n) configuration, or preferably in the 2xc3x97n configuration comprised of a still smaller number of cores for 2n strands, so that the core unit may be constructed as a unit of a volume significantly smaller than that of the superconducting coils.
In addition, since means for resetting the cores by the measurement lines for detecting the quenching of the strands is provided in the present invention, it becomes possible to stabilize the current supply through the strands.